Lets cats out being unfeeling (8)
I believe the answer is:
tactless
'unfeeling' is the definition.
(both can mean insensitive)
'lets cats out' is the wordplay.
'out' indicates anagramming the letters (out can mean wrong or inaccurate).
'lets'+'cats'='letscats'
'letscats' with letters rearranged gives 'TACTLESS'.
'being' acts as a link.
(Other definitions for tactless that I've seen before include "Lacking skill in handling delicate situations" , "Lacking sensitivity, saying the wrong things" , "Lacking sensitivity in dealing with others" , "Gaffe-prone" , "Unlikely to make Diplomatic Service" .)